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A Review on Novel Canonical Scattering Problems Solved by the Wiener-Hopf Technique with the Help of Fredholm Factorization and Network Formalism
Full text linkIn 2010s, Vito Daniele and Guido Lombardi started a new collaboration with Rodolfo S. Zich on the analysis of scattering problems in electromagnetics in spectral domain. Soon, the group selected the Wiener-Hopf technique (WHT) as one of the most promising techniques to develop new canonical solutions with physical insights (V.G. Daniele, R.S. Zich, The Wiener-Hopf Method in Electromagnetics, SciTech Publishing Inc, 2014). The development of WHT has been first extended from rectangular problems, as in classical literature, to angular region problems (V.G. Daniele, G. Lombardi, R.S. Zich, Network representations of angular regions for electromagnetic scattering, PLoS ONE, 12 (8), art. no. e0182763, 2017). Unsolvable problems of factorization were treated with the introduction of a semi-analytical general-purpose factorization method, known as Fredholm Factorization (V.G. Daniele, G. Lombardi, Fredholm factorization of Wiener-Hopf scalar and matrix kernels, Radio Science, 42(06):1-9, 2007). This tool is effective, and it aims to be a technique that avoids cumbersome mathematical specialization often encountered in WH factorization. This evolution of WHT has a strong impact in general application of the method (also in different subjects), and it has a special impact on the analysis of the physics of electromagnetism, since its semi-analytical nature maintains the spectral interpretation of the problems as analytical closed form solutions but at the same time extends the class of solvable problems (V.G. Daniele, G. Lombardi, The Wiener-Hopf Fredholm factorization technique to solve scattering problems in coupled planar and angular regions, In Advances in Mathematical Methods for Electromagnetics, pp. 279–302, SciTech Pub.-IET, 2020). Moreover, one of the main benefits of the proposed semi-analytical solutions is to allow the computation of field components by using asymptotics and analyzing spectral structural and source singularities, similarly to what is done with closed-form spectral solutions (V.G. Daniele, G. Lombardi, and R.S. Zich, The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 2. Diffraction, Modal Field, Surface Waves, and Leaky Waves, Radio Science, 52(12), pp. 1492–1509, 2017). At the same time, the development of this framework has been studied following the paradigm of Bresler and Marcuvitz (A.D. Bresler, N. Marcuvitz, Operator methods in electromagnetic field theory, Report R-495-56, PIB-425, MRI Polytechnic Institute of Brooklyn, 1956) provided for the analysis of stratified media by using transverse equation theory. We apply and extend the same methodology to represent problems of higher complexity where angular regions are combined with rectangular finite regions and stratifications (V.G. Daniele, G. Lombardi, R.S. Zich, Radiation and Scattering of an Arbitrarily Flanged Dielectric-Loaded Waveguide, IEEE Trans. Antennas Propag, 67(12), art.n.8886592, pp.7569-7584, 2019). All these types of basic geometric/material bricks, that decompose complex problems, can now be delt with WH formulations and Fredholm factorization where all equations can be represented by circuit/network modelling that allows to describe the technique with systematic steps avoiding redundancy (V.G. Daniele, G. Lombardi, R.S. Zich, Physical and Spectral Analysis of a Semi-Infinite Grounded Slab Illuminated by Plane Waves, IEEE Trans. Antennas Propag,70(12),pp.12104-12119, 2022). Examples of solved complex scattering problems are proposed in Fig. 1 and they will be discussed during the presentation
The Double PEC Wedge Problem: Diffraction and Total Far Field
Full text linkComplex scattering targets are often made by structures constituted of wedges that may interact at near field. In this paper, we examine the scattering of a plane electromagnetic wave by two separated arbitrarily oriented perfectly electrically conducting wedges with parallel axes. The procedure to obtain the solution is based on the recently developed semianalytical method known as generalized Wiener–Hopf technique that allows a comprehensive mathematical model of the problem in the spectral domain avoiding multiple steps of interaction among separated objects. The numerical results are presented to validate the procedure in terms of spectral quantities, GTD/uniform theory of diffraction coefficients and total far fields for engineering applications. The structure is of interest in electromagnetic applications, in particular, to accurately predict path loss in propagation with diffraction phenomena
Wiener-Hopf formulation of the scattering by a stepped wedge
No full textThis paper presents the formulation and the
procedure to get the solution of the scattering problem
constituted by a PEC wedge connected to a PEC step structure.
We formulate the problem in terms of generalized Wiener-Hopf
equations (GWHEs) in spectral domain whose solution is
obtained through Fredholm factorization with the help of
circuital representations of the angular region and layered
region
The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 1. Formulation and Validation
No full textComplex scattering problems are often made by composite structures where wedges
and penetrable substrates may interact at near field. In this paper (Part 1) together with its companion
paper (Part 2) we study the canonical problem constituted of a Perfectly Electrically Conducting (PEC)
wedge lying on a grounded dielectric slab with a comprehensive mathematical model based on the
application of the Generalized Wiener-Hopf Technique (GWHT) with the help of equivalent circuital
representations for linear homogenous regions (angular and layered regions). The proposed procedure
is valid for the general case, and the papers focus on E-polarization. The solution is obtained using
analytical and semianalytical approaches that reduce the Wiener-Hopf factorization to integral
equations. Several numerical test cases validate the proposed method. The scope of Part 1 is to
present the method and its validation applied to the problem. The companion paper Part 2 focuses
on the properties of the solution, and it presents physical and engineering insights as Geometrical
Theory of Diffraction (GTD)/Uniform Theory of Diffraction(UTD) coefficients, total far fields, modal
fields, and excitation of surface and leaky waves for different kinds of source. The structure is of
interest in antenna technologies and electromagnetic compatibility (tip on a substrate with guiding
and antenna properties)
The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 2. Diffraction, Modal Field, Surface Waves, and Leaky Waves
No full textTogether with Part 1, Part 2 describes the theory, the validation, and the application of
the generalized Wiener-Hopf technique (GWHT) to complex scattering problems constituted of wedges
and layers that may interact at near field. In particular, we present the full analysis of the canonical problem
where a perfectly electrically conducting (PEC) wedge is lying on a grounded dielectric slab bounded
by a PEC plane. The structure proposed in the two papers is of interest in antenna technologies and
electromagnetic compatibility (tip on a substrate with guiding and antenna properties). While the scope of
Part 1 has been to present the method and its validation applied to the problem, this paper (Part 2) focuses
on the properties of the solution and it presents physical and engineering insights. Part 2 starts from the
solution of generalized Wiener-Hopf equations (GWHEs) through Fredholm factorization in terms of an
analytical element of the spectral unknowns (Part 1), and it illustrates how to estimate physical and
engineering characteristics of the problem: geometrical theory of diffraction/uniform theory of diffraction
(GTD/UTD) coefficients, total far fields, modal fields, and excitation of surface waves and leaky waves for
different excitations (modal source and/or plane wave source)
On Circuital Modelling of Diffraction Problems in Spectral Domain
No full textThis paper summarizes and disseminates our
efforts in developing an effective technique based on Generalized
Wiener-Hopf Technique to deal with scattering problems by
canonical and complex structures through the support of
circuital modelling
Diffraction by Two PEC Inverted Staggered Half Planes
No full textThis paper presents the formulation and the procedure to get the solution of the scattering problem constituted by two Perfectly Electrically Conducting (PEC) inverted half planes who are staggered with respect to each other.
While the Wiener Hopf equations of this problem are well known, we obtain a novel solution of them by resorting to the Fredholm factorizatio
Network representations of angular regions for electromagnetic scattering.
No full textNetwork modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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